160 PRINCIPLES OF ELECTRICAL DESIGN 



k X 0.8 VZnI c T X T c (irDN,) (log ^- - l) 



TT rr 7 



For first approximations the formula may be put into simpler 

 form. 



Let A c stand for the ampere-conductors per pole pitch of arma- 

 ture periphery (A c = 2TnI c ). Let k = 2.1 (being an average 



value), and for the quantity (log e r- ~ *) P ut tne numerical 

 value 2.5, then 



E. (approximately) = (75) 



where V is the peripheral velocity of the armature in centimeters 

 per second. 



The above calculations and conclusions are based on the 

 assumption of a full-pitch winding. With a chorded or short- 

 pitch winding, the average flux density in the commutating zone 

 will be slightly reduced ; and there will be a further gain due to 

 the shortening of the end connections (ABC and A'B'C' in 

 Fig. 59). Thus the voltage generated by the cutting of the end 

 fluxes, with a short pitch winding, will be slightly less than the 

 value calculated by formula (74), or by the approximate formula 

 (75), which applies to a full-pitch winding. 



49. Calculation of "Slot Flux" Cut by Coil during Commuta- 

 tion. A reference to the diagrams of flux distribution in the 

 commutating zone (Figs. 57 and 58) will make clear the fact that, 

 even when the effect of the end connections is neglected, the 

 center of the neutral commutating zone is not the point on the 

 armature periphery where flux neither enters nor leaves the teeth ; 

 because in order that the short-circuited conductors shall not 

 cut the slot leakage flux, this flux must be provided by the 

 main field pole toward which the brushes are shifted to obtain per- 

 fect commutation. The point on the armature periphery where 

 flux neither enters nor leaves the teeth may be found by drawing 

 curves representing the magnetomotive forces exerted by field 

 poles and armature windings at every point on the armature 

 periphery, and where the sum of the ordinates of such curves is 

 zero the surface flux density must also be zero. The brushes 

 must, however, be moved forward beyond this point until the 

 reversing flux entering the teeth comprised in the brush arc has 



